Signal translating apparatus



Jan. 7, 1941. F. MASSA v SIGNAL TRANSLATING APPARATUS 2 Sheets-Sheet 2 Filed NOV. 28, 1936 FREQUENCY IN CYCLES O ,O z 2 m m a 10a 1000' 10000 mwentor FREQUENCY IN GYCLEJ' v Mass Gttorneg- Patented Jan. 7, 1941 UNITED STATES PATENT OFFICE SIGNAL TRANSLATING APPARATUS Frank Massa, West (lollingswood, N. .L, assignor to Radio Corporation of America, a corporation of Delaware Application November 28, 1936, Serial No. 113,120

1 Claim.

(1) For an efficient high frequency speaker, the

m mass of the voice coil should be relatively "small. (2) For an efficient low frequency speaker, the mass of the voice coil should be relatively large.

(3) To improve the efficiency of the system at high frequencies, the voice coil conductor should be made of aluminum.

From various studies which I have made, I have found that the above ideas are not generally true. Contrary to popular belief, I have found that, in order to obtain maximum efficiency in a high frequency loudspeaker, the mass of the voice coil should be greater than the mass of the remainder of the vibrating system. I have also found that using an aluminum voice coil will actually decrease the efliciency of a loudspeaker at all frequencies (although mostly at the higher frequencies) if its mass is less than approximately one-third of the effective mass of the remainder, of the vibrating system. Under this condition, I have found that it is best to employ a copper voice coil instead of an aluminum voice coil. I have also found that, at low frequencies, voice coils which are lighter than the effective mass of the remainder of the vibrating system will give relatively high efficiencies and that it is not necessarily required to employ a Voice coil the mass of which is greater 0 than the mass of the remainder of the vibrating system in order to obtain good low frequency efficiency. In fact, my studies have shown that such conditions are only slightly beneficial at low frequencies, and that these conditions, which 5 have been heretofore regarded as detrimental to good efficiency at the higher frequencies, may actually provide more efficient performance at the higher frequencies as well. i The primary object of mypresent invention, therefore, isto provide an improved method of designing an electro-dynamicloudspeaker to provide maximum. efiiciency over. a wide range.

More specifically, it is an object ofmy present invention'to provide an improved loudspeaker which will give not only more efficient reproduction at the high frequency en d as well as at the low frequency end, but which will also be capable of reproducing signals more wider range than heretofore.

faithfully over a In carrying out my invention, I preferably employ different speakers for the low frequency region and for the high frequency region. For

the'high frequency speaker, I

propose to use an aluminum voice coil Whose mass is the larger part of the mass of the vibrating system, while for the low frequency speaker I have found that it is not appreciably detrimental to the efiiciency of the loudspeaker to have the voice coil mass smaller than the mass of the cone or other equivalent vibrating element. at all, if a loudspeaker is built voice coil in which the mass of aluminum is less than approximately one-third At any frequency with an aluminum the efiective mass of the remainder of the vibrating system, a gain in efficiency will result if 'thealuminum coil is replaced by a copper coil. In

other words, if the practical considerations involved in .the design of a loudspeaker require that the voice coil be made small, the voice coil may be made of copper and serve more efficiently in accordance with my pres cases in which an aluminum than approximately one-third at any frequency, ent invention, for coil would be less the effective mass of the remainder of the vibrating system.

The novel features that I consider characteristic of my invention are set forthwith particularity in the appended claims. self, however, together with The invention itadditional objects and advantages thereof, will best be understood from the following description nection with the accompan which when read in conying, drawings in Figure 1 is a simple diagrammatic view showing the general construction of a horn type loudspeaker having an electro-dynamic driver, and

with reference to which the m athematical analysis set forth below will bemade,

Figure 2 is the equivalent electrical analogue er of Fig. 1,

Figure 4 is a graph showing which indicate the maximum a family ofcurves efficiencies obtainable at various frequencies and flux densities in a horn loudspeaker employing a copperc'voice coil,

Figure 5 is a' graph similar to Fig. .4 but indicating maximum efficiencies when the voice coil is made of aluminum,

Figure 6 is a graph showin E; the efficiency, at

several frequencies, of a loudspeaker employing an aluminum voice coil, the several curves showing efficiencies obtainable when the mass of the voice coil is changed with respect to the effective 5 mass of the entire vibrating system, and

Figure '7 is a diagrammatic view of a double voice coil loudspeaker formed in accordance with my present invention.

It has long been recognized that, for reproduc- 10 tion of low frequencies, it is best to employ a loudspeaker having a large diaphragm or cone in order to radiate acoustic energy with minimum distortion. On the other hand, for the reproduction of high frequencies, it has been found de- 5 sirable to employ a loudspeaker having a small diaphragm or cone in order to eliminate throat phase interference in the throat of the particular horn used and also to prevent the diaphragm from breaking up, since it is generally desirable 20 to have the diaphragm vibrate as a piston so that subharmonics will not be generated. Moreover, for a given cone, it has been found that the throat area of the horn should decrease as the frequency increases if maximum efficiency is to be obtained 535 at all frequencies. It is obvious, however, that in practice, it is hardly possible to provide a single speaker which will meet all these requirements, and for this reason, a compromise must be struck in order to provide a practical loudspeaker. One

such loudspeaker is illustrated in Fig. l and comprises a horn I supported by a suitable support 3 which also flexibly supports a cone 5 within a chamber 1. The cone 5 constitutes an element of an electro-dynamic speaker and is actuated in 35 response to the interaction of a variable magnetic field set up by signal currents flowing in a conducting coil 9 and a steady magnetic field set up by suitable flux providing structure (not shown) having an air gap in which the conducting coil 40 9 is movably mounted.

To facilitate an understanding of the elements of the structure shown in Fig. 1, reference may be had to its electrical analogue shown in Fig. 2, wherein so mo/ mu eifective mass of the voice coil 9 and the cone 5 in grams.

Ac=effective area of the cone 5 in sq. cms.

rA=acoustic resistance of the horn I=l2/Ah, and

An=area of horn I at the throat in sq. cms.

By substituting numerical values, the equivalent circuit in Fig. 2 can be easily solved to show, quantitatively, the performance of the loud- 70 speaker at various frequencies. The voltage to be assumed acting in the circuit is equal to BZi/IOAC, where B=air gap flux density in gauss, l=length of voice coil conductor in cms., i: amperes flowing through voice coil conductor.

75 Using this value of equivalent voltage, the power computed flowing through TA is equal to the acoustic power radiated by the speaker.

Looking more critically at the equivalent circuit of Fig. 2, it can be seen that the value of the capacitance CA1 should be made high enough so 5 that its impedance is low compared with the value of wM at the lowest frequency which must be reproduced. If, however, a peak is desired in the output at some part of the frequency range, the capacitance CA1 may be adjusted so that it 10 will resonate with wM at the desired frequency. When this is done, the output will drop off at frequencies below resonance.

The effect of the capacitance CA2 is to cause a loss in output at frequencies above which its reactance becomes comparable in magnitude to the throat resistance. To preserve good high-frequency response, therefore, the throat volume of the horn i should be kept very small so that its reactance at the highest frequency of reprocluction is high compared with the throat resistance.

Assuming that CA1 and CA2 are so designed that they do not influence the performance of the speaker in its working range, it can be seen from Fig. 2 that maximum radiation efiiciency at a given frequency will occur when wM =11. Thus, the optimum size of horn throat for a given cone follows directly.

In order to derive a mathematical equation from which maximum possible efficiency of a loudspeaker such as that described heretofore may be realized, reference will now be made to the circuit shown in Fig. 3 of the drawings, and the following assumptions will be made in the mathematical analysis:

1. That the horn I shall'be of exponentially increasing cross section, with a cut-off frequency lower than the frequency being radiated by the cone 5. m

2. That the mouth of the horn I shall be large enough so that no reflections occur as the sound wave emerges from it.

3. That the vibrating system driving the horn shall be a pure mass; that is, the stiffness of the diaphragm or cone mounting shall be low enough to make its resonant frequency lie below the frequency being generated in the horn; and the stiffness in the throat chamber (or the chamber between the horn throat and the cone 5) shall be high enough so that its impedance is higher than the horn throat resistance at the frequency being radiated.

4. That each portion of the cone 5 moves in phase, and

5. That the voice coil is a pure electric resistance.

Let it also be assumed that the following constants apply to the horn loudspeaker of Fig. 1:

i=root mean square amperes flowing through the voice coil 9, rn=electrical resistance of the voice coil in ohms, Z=length of conductor in voice coil 9 in cms., B=flux density, in gauss, of the air gap in which the coil 9 is located, m1=voice coil mass in grams (excluding the mass of the insulation), m2=mass of the cone 5, plus the mass of the voice coil form and insulation, plus the air load, in grams, Ac=area of cone 5 in sq. cms., and Ah=area of the horn throat in sq. cms.

It is obvious that the electric energy which flows into the voice coil 9 is used up in part as heat dissipation in the voice coil and part is converted into sound energy at the throat of the horn. The efiiciency of the loudspeaker will be defined as the ratio of the acoustic power output to the electric power input, which, expressed mathematically, becomes Efiiciency= X 100 (1) Where Pn=electric Watts input to the voice coil 9, and PA=acoustic watts output from the horn I.

In order to more clearly see the conditions which exist during the transfer of electric energy to acoustic energy in the loudspeaker, the equivalent electric impedance presented to the circuit by the system of Fig. 1 is shown in Fig. 3. In Fig. 3, am is the electric impedance appearing in series with the ohmic resistance of the voice coil due to the mechanical impedance of the vibrating system. This impedance is called motional impedance and is made up of a resistive and a reactive component. In the absence of mechanical losses, the real component represents the acoustic radiation resistance presented by the horn.

It can be easily shown that the magnitude of the motional impedance is equal to B l X 10 vector electric ohms where zm=mechanical impedance of the vibrating system in mechanical ohms.

For the case assumed, in which mechanical losses have been neglected and both the compliance of the diaphragm suspension and horn throat chamber are not assumed to be of consequence in the frequency range concerned, it follows that zM:rM+9'w m1+m2) mechanical ohms (3) where nvi=mechanical resistance presented to the diaphragm by the horn,

w=21rf, and f=frequency of vibration in cycles per second,

and

' 0A 2 TM -mechanica1 ohms where =density of the medium into which sound is being radiated, in grams/00., and

c=velocity of sound in the medium in cm./sec.

For air under average conditions,

r Ah "mechanical ohms Substituting Equation 5 in Equation 3 and then the result in Equation 2-, the motional impedance becomes Wench-i0 ohms (6) Referring again to Fig.3, it is obvious that the total electric power input to the circuit for the current i is PE=i (rE+TEM) watts (7) and the acoustic power radiated is PA=i TEM watts (8) Dividing Equation 8 by Equation 7, the efficiency becomes Substituting Equation 6 into Equation 9 and letting K=B z 10 10) and 42A? TM: Ah

the efficiency becomes It can be seen from an inspection of Equation 12' that, for a given speaker, as the frequency increases, the efficiency decreases. To obtain the maximum possible efficiency at any particular frequency, Equation 12 may be diiferentiated with respect to m, keeping w and (m1+m2) constant and placing the derivative equal to zero, as follows:

which gives, as the condition for maximum efficiency at a given frequency,

rM=w(m1+'m2) (14) Substituting Equation 14 in Equation 12 gives Let m2=km1 (16) where k is a numerical ratio. Then (m1+mz) =(1+k)m1 (17) Also m1=DlA (18) where j D='density of the voice coil conductor 9 in grams/cc.

L=length of the voice coil conductor 9 in cms.

A=cross section of the voice coil conductor 9 in sq. cms.

and

J21 TE- where R=resistivity of the conductor 9 in ohms/cc.

Substituting EquationslO, 1'1, 18, and 19 into Equation 15, the maximum possible efficiency at any frequency becomes B2 HfW where B=fiux density, in gauss, of the air gap in which the coil 9 is mounted,

f=frequency in cycles per second,

k=ratio of cone plus voice coil form and insulation, plus air load mass to voice coil mass,

D=density of the voice coil conductor in grams/cc,

R=resistivity of the voice .coil conductor in ohms/cc.

It must be emphasized that the maximum efficiency in Equation 20 can only be realized at a given frequency provided that Equation 14- is also satisfied at that frequency. This means that to secure maximum efficiency at all frequencies for a given vibrating system, the throat area of the horn should vary inversely as the frequency. For a fixed horn throat, however, the efilciency will be less than shown by Equation 20 at every frequency except for one frequency which satisfied Equation 14. The actual values of efiiciency for a fixed throat at other frequencies may be found from Equation 12.

The purpose of deriving Equation 20 is to show how the various components of a horn loudspeaker are effective in determining the maximum efficiency which can be realized at various frequencies. In Figs. 4 and 5, there are shown two families of curves in which the maximum efficiency at each frequency was computed for both copper and aluminum voice coils. For the solid curves, k=0, which assumes the hypothetically ideal case in which the total mass in the vibrating system is in the voice coil conductor. For the dotted curves, k=1, which assumes that the voice coil mass is one-half the total effective mass of the vibrating system. This latter assumption is more nearly representative of what can be met in actual practice, but even for the hypothetical case represented by the solid curves, it is evident that to secure high efiiciency at very high frequencies requires materials which can either cause an increase in the air gap flux density to a value considerably above 20,000 gauss, or can provide a conductor for the voice coil 9 which has a much lower density-resistivity product than aluminum.

Equation 20 brings out the further fact that, at the higher frequencies, where the efficiency is inherently low (left hand member of the denominator predominating), it is of vital importance to make is as small as possible, which means that the voice coil mass should be as large as possible for good performance. At the lower frequencies, when the efiiciency is inherently high, it is obvious that it is not necessary to make 10 very small. This means that the voice coil mass can be smaller than the cone mass, at low frequencies, without appreciable sacrifice in efficiency. On the other hand, the voice coil mass should be higher than the cone mass at the higher frequencies to secure best performance.

The foregoing conclusions may also be stated from a, slightly different point of view. From Equation 20, it can readily be seen that the efficiency increases as k (which equals as seen from Equation 16 supra) decreases.

Thus, it follows that the efficiency of a horn loudspeaker at any frequency actually increases as the voice coil mass increases for a given conductor material (this effect being more pronounced with increasing frequencies), which is a, fact contrary to popular belief. High efiiciency is not obtained because of the low mass of the conductor or coil 9, but rather because of the low density-resistivity product of the material thereof. At the low frequency end, there is little to be gained by employing aluminum in place of copper for the voice coil, and, as a matter of fact, the efficiency of the speaker may even be lowered if the change is made in a particular speaker whose air gap volume has been fixed. In other words, by filling a given volume of air gap with copper instead of aluminum, a higher efficiency generally results at the low frequencies because of the relatively high mass of low frequency coils. It is even possible that the same condition may occur at the high frequencies, depending upon the relative change in the expression (l-i-Ic) as compared with the expression DR. in Equation 20. Thus, it follows that aluminum cannot be used indiscriminately in place of copper in the voice coil Q to obtain high frequencies, and in many cases, the substitution may even be detrimental.

From the curves shown in Figs. 4 and 5, it will be obvious that, for equal values of k, aluminum is preferable to copper at all frequencies. It must be remembered, however, that to obtain the same value of k for an aluminum voice coil, about 3.3 times the volume of conductor is required. For a fix-ed volume of conductor, the relative merits of aluminum as against copper will depend upon the corresponding values of k as above described.

Referring, now, to Fig. 6, there are shown, in this figure, three curves I, II and III showing, respectively, the efficiency of a loudspeaker for cycles, 1,000 cycles and 10,000 cycles when the value of k is varied, is being smaller than unity when the voice coil mass exceeds the eifective mass of the remainder of the vibrating system, greater than unity when its mass is less than the mass of the latter, and equal to unity when its mass equals the mass of the latter. For values of is less than unity, it will be seen, from curve I, that there is negligible gain in efficiency by using a relatively massive voice coil. However, curve III shows that a considerable gain in efficiency may be obtained by making 7c less than unity.

The foregoing analysis also leads to another important discovery which I have made. For example, if, in a loudspeaker provided with an aluminum voice coil, the mass of which is less than approximately one-third of the effective mass of the remainder of the vibrating system, the aluminum voice coil is replaced by one of copper, a gain in efficiency will result. In other Words, as stated heretofore, if the practical considerations involved in the design of a loudspeaker of the type under consideration require that the voice coil be made small, copper may be used for the voice coil at any frequency for cases in which an aluminum voice coil would have a mass less than approximately one-third the effective mass of the remainder of the vibrating system.

In Fig. 7, there is shown a diagrammatic view of a loudspeaker built upon the principles heretofore set forth. The cone or diaphragm H, which is preferably made with a small section ll for radiating high frequencies and a larger section H which moves with the section H at the lower frequencies only, may constitute part of a horn loudspeaker system with its front surface feeding into a high frequency horn (not shown) and its rear surface feeding into a low frequency horn (also not shown). For actuate ing the cone 1 I, I employ two separate voice coils i3 and I5 carried by the voice coil form sections l1 and I9 which are connected by a compliant coupling 2| in well known manner. The coil [3 is made of copper'and is relatively massive to provide high eificiency at the lower frequencies, while the coil l5, placed immediately adjacent the diaphragm II, is made f aluminum, with a mass preferably greater than the mass of the small section ll of the speaker diaphragm. A loudspeaker so constructed and capable of reproducing a range of frequencies which includes frequencies of 500 cycles and over, will operate much more efficiently not only over the lower range (1. e., below 500 cycles) but at the higher frequencies (i. e., above 500 cycles) as well.

Although I have described my present invention in considerable detail and have shown it applied to but one form of loudspeaker, I am fully aware that many other forms of loudspeakers can be designed incorporating the teachings hereof. In fact, in my copending application Serial No. 113,475, I have shown several forms of horn type electro-dynamic loudspeakers in which the principles herein set forth in detail may be incorporated. I therefore desire that my invention shall not be limited except insofar as is made necessary by the prior art and by the spirit of the appended claim.

I claim as my invention:

An electro-dynamic loudspeaker having a vibrating system which includes a vibratible element and an electrically conductive driving coil therefor, the maximum efficiency of said loudspeaker at any frequency being defined by the equation 41rf(1 +16) DR +12 X 10- where B is the flux density of the air gap in of the expression (1+k) and the expression DR is a minimum.

FRANK MASSA. 

